American Mineralogist, Volume 77, pages 345-358, 1992

Chemical analysis of actinolite from reflectance spectra

Jonx F. Musunn Department of Geological Sciences,Box 1846, Brown University, Providence,Rhode Island 02912, U.S.A.

Ansrn-c.cr Reflectancespectra of medium (0.005 pm between 0.3 and 2.7 pm) and high (0.0002 pm between1.38 and 1.42pm and 0.002 pm between2.2 and2.5 pm) spectralresolution of 19 from the -actinolite solid solution seriesare used to characteiue systematic variations in absorption band parametersas a function of composition. The medium-resolution data are used to characterizebroad absorptions associatedwith elec- tronic processesin Fe3+and Fe2*, and the high-resolution data are used to characterize overtones ofOH vibrational bands. Quantitative analysesofthese data were approached using a model that treats absorptions as modified Gaussiandistributions (Sunshineet al., 1990). Each spectrum was deconvolved into a set of additive model absorption bands superimposedon a reflectancecontinuum. For absorptionsassociated with electronic pro- cesses,the model bands were shown to provide estimates of the Fe and Mg chemistry with correlations of greater than 0.98. The systematic changesin the energy, width, intensity, and number of OH overtone bands are easily quantified using the mod- ified Gaussian model, and the results are highly correlated with the FelMg ratios of the samples.These results indicate that the modified Gaussianmodel can be used to quantify objectively the bulk chemistry of the minerals of the tremolite-actinolite solid solution seriesusing high-resolution reflectancespectra ofthe OH overtone bands.

INrnooucrroN into realistic probability distributions. In the analyses Extraction of quantitative geochemicalinformation is presentedhere, a similar approach is applied to the ab- vibrational pro- an important goal in reflectancespectroscopy, both as a sorptions associatedwith electronic and the tool for rapid and nondestructivelaboratory analysesand cessesin calcic and, more specifically, for interpretation of remotely obtained observations of minerals of the tremolite-actinolite-ferroactinolite solid very in the Earth and other solid bodies in the solar system.The solution series. Calcic amphiboles are common chemical and crystallographicbases for the interpretation terrestrial geologic terranes, especially mafic and ultra- ofabsorption bands in reflectancespectra are reasonably mafic terrane,and specificcompositions often can be used well understood(e.g., Burns, 1970;Farmer,1974;Hunt, to infer physical conditions of mineral and forma- (e.g., Annersten, 1977). The assignment of a particular absorption to a tion Laird and Albee, l98l; Skogbyand goal specificcrystallographic site geometryand absorbingspe- 1985).The of this investigationis not only to model cies have proven consistent acrossa large range ofcom- the specificabsorptions associated with calcic amphiboles provide processes positions and structures.This knowledgehas been but also to insight into the absorption general min- extremely valuable for the remote identification of min- in that can be used in the analysisof other groups. eral specieson other planets(e.g., Pieters, 1986; McCord erals and mineral Background discussionsofac- pro- et al., 1982).However, there have been few detailed anal- tinolite crystal structure, chemistry, and absorption presented yses to determine quantitative associationsbetween the cesses are below, followed by a detailed position, shape,and strength of absorption bands in re- discussion of the modeling approach. The results of the presented flectancespectra and the chemical composition of min- modeling of the reflectance spectra are then model erals.A sound understandingofthe relationship between with an emphasistoward the associationbetween absorption band parametersand specific mineral chem- parametersand sample chemistry. istry would have a broad range of applications in the reduction and analysis of remotely obtained and labora- Actinolite crystal structure and chemistry tory reflectancespectra. Understanding of the variability of the reflectance One desiresa method of deconvolving reflectancespec- spectra shown in Figure I requires a basic knowledge of tra into concentrationsofabsorbing speciesthat produces crystal structure and chemistry. The idealized actinolite quantitative results and is generalin approach. Sunshine chemical formula, Car(Mg,Fe)rSisorr(OH)r,is rarely en- et al. (1990) have made some progressin this area by countered with natural samples.There are generally ap- deconvolving Fe2*absorptions in pyroxenesand olivines preciable amounts of Al3*, Fe3*,Mn, Cr, and Na in these 0003404x/92l0304-o345$02.00 345 346 MUSTARD: ACTINOLITE ANALYSES FROM REFLECTANCE SPECTRA

1

o o 17- G' 4' C) (D 7 (r(l) 1 5 2 0 1'/

FawavetSfiogtn, 112 'ow.rrt3tf,gtn .pf, Infm in a generalprogression from high-Fe samplesnear the bottom to low-Fe samplesnear the top. (a) Data obtained at a sampling resolution of 0.005 pm. The number adjacent to each spectrum 0.30 0.60 o.g0 1.20 t.50 1.80 z1o 240 near 0.6 pm refersto the samplenumber, and the numbers near WavelengthIn /rm 1.5 pm give the percent reflectanceof each sample at 1.5 pm. (b) Reflectancespectra obained at a sampling resolution of 2 A Fig. 1. Reflectancespectra of 19 samplesfrom the tremolite- between 1.38 and 1.43 pm; (c) data obtained at a sampling res- actinolite solid solution series.All data have beenoffset for clar- olution of 0.002 pm between 2.2 and 2.45 rrm. The numbers ity approximately 50/orelative to each other. The numbers on betweenb and c indicate the samplenumber of the spectrajoined the left side of each plot indicate the reflectancescale. There is by the solid lines.

minerals. The actinolite crystal structure is monoclinic shown that Fe2* is enriched in Ml and M3 relative to with space group C2/m and consists of two unique tet- M2 in calcicamphiboles (Burns and Prentice,1968; Ernst rahedralsites (Tl, T2), four unique octahedrallycoordi- and Wai, 1970;Wilkens et a1.,1970; Wilkens, 1970).Mg nated sites(Ml, M2, M3, and M4), and one l2-coordi- showsa site preferencethat is complementaryto Fe2*.Ca nated site (A) (Ghose,l96l). almost exclusively occupiesthe M4 site, but there is rare- Site populations are complex in amphiboles (seeHaw- ly enough Ca to fill this site completely. Vacant M4 sites thorne, 1983, for a review) and are important for the are preferentially filled by available Mn and Fe2*. interpretation and quantifi cation of actinolite reflectance spectra.Al3* shows a site preferencefor Tl when in tet- Sourcesof absorption in calcic amphiboles rahedral coordination and the M2 site when in octahedral Three basic processesare responsible for the suite of coordination. Fe3*,like Alr*, exhibits a preferencefor the absorptions observed in the spectra shown in Figure l. M2 site (Wilkens, 1970; Hawthorne, 1983; Skogbyand Excitation of d-orbital electronsin transition metal ions, Annersten,1985). However, local chargebalance can in- particularly Fe, is primarily responsiblefor the broad ab- fluencethese general distributions. Although Fe2+can oc- sorptionscentered between 0.85 and 1.2 p.m.The broad cupy any ofthe four octahedral sites and the specificor- absorption centered near 2.45 pm is largely due to an dering among thesesites is complex, severalstudies have electronic transition. Absorptions involving transfer of MUSTARD: ACTINOLITE ANALYSES FROM REFLECTANCE SPECTRA 347 electrons between anions and cations generally exhibit Burns and Strens,1966; Bancroft and Burns, 1969;Wil- band minima at wavelengthsless than about 0.5 pm, but kens, 1970;Burns and Greaves,l97l;Law,1976). The wings ofthese absorptions do extend through the visible wavelength position of the OH- stretching fundamental to the near infrared. Cation-to-cation chargetransfer ab- dependson the cation occupancyof the two M I and one sorptions can have well-defined visible to near infrared M3 sites as a unit. For an ideal actinolite solid solution, absorptions. Finally, overtones and combination over- there are four unique distributions: A : (MgMgMg), B : tones of fundamental vibrational bands associatedwith (MgMgFe), C : (FeFeMg),and D : (FeFeFe).Since each OH ions account for the narrow featuresnear 1.4 rrm ond results in a distinct absorption, there are four possible at wavelengthslonger than 2.0 pm. Details of each cate- OH- stretching fundamentals in a simple Fe-Mg amphi- gory of absorption and relationship to cation and anion bole system.Additional bands can be expectedif the Ml site occupancyare discussedbelow. and M3 sitesare occupiedby other ions (e.g.,A13*, Fe3*) Electronic transitions. The energy ofelectronic transi- or the A site is occupied by Na or K. tion absorptions is determined by the crystal field split- The narrow absorptions between 2.2 and 2.5 pm (see ting, whereasthe intensity or strength ofthe absorptions Figs. la and lc) are combination overtonesinvolving OH- is governedby probability considerationsdetermined pri- stretching vibrations and metal-OH- bending modes marily by site distortion and symmetry (Burns, 1970; (Hunt, 1977).Although the location of the fundamental White and Keester,1967). The broad, indistinct absorp- metal-OH bendingmodes is reasonablywell known (500- tions between0.85 and 1.2 p.mare generallyassigned to 800 cm-'or 12-15 pm), there has been little work to Fe2* electronictransitions in Ml, M2, and M3 (Haw- quantify relationships between parameters that charac- thorne, 198l). However, little has beendone to quantify terize absorption and chemistry or crystal structure. An further the exact assignmentofthese bands becausethese increase in the wavelength position of the fundamental three sites are so similar in general size and shape that bending modes with increasing Fe content has been ob- individual electronic transitions in these sites are proba- servedby Kukovskii and Litvin (1970) and Barabanov bly not resolvable.Goldman and Rossman(1977) dem- er al. (1974). onstrated that Fe2*in the M4 site is primarily responsible for the deep, well-resolved1.0- and 2.4-pm bands ob- Approach to quantitative analysis servedin transmission spectraof actinolite and tremolite. The general systematicsof the reflectancerelative to These absorptions are extremely intense becausethe M4 compositionare simple.Samples with the most Fe2*(21, site is very distorted and lacks a center of symmetry. 20, ar,d 8) have deeperand broader absorptions between Although Ca and Mn occupy this site with greater effi- 0.8 and 1.2 p.m relative to sampleswith the least Fe'z*(9 ciencythan Fe2*,Goldman and Rossman(1977)interpret and l2), and sampleswith abundantFe3* (e.g., 8, 19,and the results as indicative ofa strong preferenceofFe2* for 2 I ) exhibit more intense chargetransfer absorptions rel- this site. Other ions that exhibit absorptions due to elec- ative to sampleswith little Fe3*(9a, 9, and l2). However, tronic transitions in this wavelengthregion are Fe3*,Cr3*, the association between absorptions and chemical com- and Mn2*. In the data shown in Figure l, the weak, nar- position in reflectancespectra has been difficult to quan- row features between 0.3 and 0.6 pm are due to spin- tify. Some successhas been achieved in simple solid so- forbidden electronic transitions in Fe2* and Fe3*. Cr3* lution serieslike (Adams, 19741,Hazenet al., absorptions are observed in spectrum 13, shown in Fig- 1978)and olivines (Hazenet al., 1977;'King and Ridley, ure la, and are centerednear 0.45 and 0.6 1rm. 1987) relating band minima and band areasto chemistry. Charge transfer. For the actinolite samplesstudied here The complex substitution and number of unique absorb- the predominant intervalencecharge transfer absorptions ing sites in the minerals of the tremolite-ferroactinolite are between Fe2*and Fe3+.These account for the absorp- series preclude the use of such simple characterizations tions of variable intensity centered between 0.6 and 0.8 of absorptions. Investigators have modeled crystal field pm. For charge transfer absorptions to occur, the ions absorptions assumingthat the absorptions have a Gauss- must be in adjacent crystallographicsites, either edge-or ian distribution in energy (Smith and Strens, 1976;Farr face-sharedpolyhedra, and the direction ofseparation be- et a1.,1980; Clark, 198l; Roushand Singer,1986; Hu- tween the sites must be parallel to the electronic vector gueninand Jones,1986). However, these applications re- of the incident radiation (Allen and Hush, 1967; Smith quired two overlapping bands to model adequately ab- and Strens, 1976).Crystallographic arguments and Miiss- sorptions thought to be the result of a single electronic bauer analysesindicate that Fe3* shows a preferencefor transition, and they failed to produce results that could the M2 site. Since the M2 site sharesat least one edge be related to composition. with the other three sites,this cation-to-cation absorption Sunshineet al. (1990)have critically evaluatedthe use is expectedto occur freely. of Gaussians to model electronic transitions and have Vibrational bands. The sharp, narrow absorptions ob- proposeda modified Gaussianmodel (MGM). The phys- served in the spectra shown in Figure lb are overtones ical basis of this model is as follows. The energypotential of the fundamental OH- stretchingabsorptions that occur of any absorbing ion in a given site can be approximated between 2.7 and 2.8 p.m. The fundamentals have been as a harmonic oscillator when perturbed by photon in- the subject of many studies of calcic amphiboles (e.g., teractions. A harmonic oscillator has a Lorentzian distri- 348 MUSTARD: ACTINOLITE ANALYSES FROM REFLECTANCE SPECTRA bution in energy becauseof exponential damping in the properties. The sampleswere inspectedunder an optical time domain. However, absorption bands in reflectance microscope for homogeneity. Major element oxide con- spectra are due to photon interactions with millions of centrations,presented in Table l, were measuredwith the unit cells that, becauseof crystal defects, vacanciesand microprobe facility at Brown University. TiO, content substitutions, and thermal vibrations, have a Gaussian was also measuredbut is not reported in Table l, since distribution of bond lengthsabout a mean. Thereforebond the concentration of this oxide was always at or below length is a random variable. Since bond length deter- the sensitivity limits of the microprobe (0.010/o).F..* mines the energy of absorption, a Gaussian distribution content was analyzed by volumetric microtitration of bond lengths will result in a statistical distribution of (Thornberet al., 1980).Fe3* content was then calculated absorption energies.The key parameter to determine is from the total Fe analyzedby the microprobe using sim- the mathematical description of the distribution of ab- ple massbalance: sorption energies. FerO, : (FeOo."*- FeO,,*.i"")x l.l l13. Sunshineet al. (1990) modeled absorptionsin trans- mission and reflectancespectra ofclino- and orthopyrox- Two titrations were performed on each sample and were ene with a Gaussian equation. These pyroxenes exhibit averaged(Skoog and West, 1982).An evaluationof the two dominant electronic transition absorptions,one near uncertainty in titrations was made using laboratory stan- 1.0pm and the other near 2.0 1rm.Since each absorption dard material TRSl38-9D2 (suppliedby J. G. Schilling is thought to be due to a singleelectronic transition (Burns, of the University of Rhode Island). Five samplesof the 1970),any realisticmodel shouldrequire only one band standard titrated with eachbatch ofunknowns yielded an to describeeach absorption. The classicalGaussian mod- averagevalue of 7.67 -r 0.12 wto/oFeO (acceptedvalue el of band shaperequired two overlapping bands to mod- 7.75 wto/oFeO, Gwinn and Hess, 1989).An additional el these single absorptions, and the results failed to pro- three actinolite sampleswere loaned by R. G. Burns for duce any correlations with chemistry. Crystal field theory measurementof the spectral properties. Chemical anal- statesthat the energyof electronic absorptions is propor- ysesof these sampleswere performed elsewhere,and ref- tional to cation-anion bond length raised to the nth pow- erencesfor theseanalyses are given in Table l. Basedon er (Burns, 1970;Marfunin, 1979).Therefore Sunshine et these general site preferencesand the method of Robin- al. (1990) modified the Gaussianequation to include an son et al. (1982\, the oxide concentrations are cast into exponent for the energy term. They empirically deter- site occupancyassignments in Table l. Thesesite assign- mined the best value for the exponent as - I by fitting ments and populations are approximate, and precisede- single electronic absorptionsin orthopyroxene.The same terminations require detailed and coordinated Mdss- exponent also applies to single electronic absorptions in bauer, X-ray, and infrared techniques. clinopyroxene. From this relationship it is inferred that the potential energy of a site is dominated by the Cou- Bidirectional reflectancespectroscopy lombic potential energy. All reflectancespectra used in this analysis were ob- The resultsofSunshine et al. (1990) indicate that the tained with the RELAB spectrometer,a high-resolution MGM is a significant advance over previous modeling bidirectional spectrometerat Brown University support- approaches for reflectance spectra. The model was ap- ed by NASA as a multiuser facility. RELAB is designed plied successfullyto mineral mixtures to deter- to obtain reflectancemeasurements at specific angles of mine end-member concentrations(Sunshine and Pieters, incidenceand emergence,defined by the user,to simulate l99l), to characterizeolivine composition in the forster- geometriesused in the acquisition of data by instruments ite-fayalite solid solution series (Sunshine and Pieters, on spacecraft,aircraft, and telescopes.These unique ca- 1990), and to separatethe end-member reflectancespec- pabilities also permit the investigation of the angular dis- tra of mineral components in an intimate mixture (Mus- tribution of light due to scattering,transmission, and re- tard, l99l). In the analysespresented here, the MGM flection off a surface. Detailed descriptions of the model is used to characterize the complex overlapping instrument are given by Pieters (1983) and Mustard and electronic transition and charge transfer absorptions in Pieters(1989). Briefly, a beam of monochromaticlight is low-resolution spectraand the overtone and combination focused on the sample at a specific angle of incidence overtone OH absorption in high-resolution spectraofac- between 0 and 60" to the surface normal. The reflected tinolite. Although the MGM model was not developed radiation is detectedusing a cooled photomultiplier tube specifically to model OH or chargetransfer absorptions, for ultraviolet to visible wavelengthsand an indium-an- the generalprinciples behind the MGM model apply. timinide detector for longer wavelengths,at emergence anglesbetween -60 and 60". RELAB has a practical op- erating wavelengthrange ExpnnrvrrNTAI, pRocEDURES of between0.3 and 3.7 1rmwith an averagespectral resolution of 3.2 nm. The instrument Samples precision is better Ihan 0.25o/o,which is smaller than po- Sixteen samplesthat can be reasonablyassigned to the tential systematicerror due to diffraction or sample prep- tremolite-actinolite-ferroactinolite solid solution series aration. Raw data are normalized to measurementsob- were acquired for analysis of the spectral and chemical tained simultaneously of pressed halon, an inert MUSTARD: ACTINOLITE ANALYSES FROM REFLECTANCE SPECTRA 349 fluorocarbon that is uniformly bright between 0.25 and 2.7 um. Theserelative reflectancedata are then calibrated o o to absolute reflectanceusing the calibration factors for c halon given by Weidner and Hsia (1981). o I Samples were measured at 5-nm sampling resolution IE o between0.3 and 2.7 prn, aL2-A samplingresolution be- G tween 1.35and I .45 pm, and at 2-nm samplingresolution C' between2.2 and2.5 pm. The low-resolution spectraldata I (5 nm) are used to characterizebroad absorptions asso- 6 ciated with electronic processes,whereas the high-reso- € lution data Q 4,2 nm) are usedto characteize the sharp, = narrow absorptionsassociated with vibrational processes. A standard viewing geometry with an incidence angle of 30' and emergenceangle of 0o was used in all measure- ments. The sampleswere ground with a mortar and pestle to enhance the intensity of spectral features. Since the total amount of some samples was very limited, no at- g o tempt was made to isolate a particular gain-size fraction. The particle diameters of the samplesare in generalless rtrI o than 250 pm in size with a sizeablefraction of the par- E ticles lessthan 30 1rm.About I g of sample was required to fill the sample dishes,which were I cm in diameter by E 5 mm deep. Low-resolution, full wavelength spectra are 6 3 shown in Figure la, high-resolutionspectra ofthe 1.38- o 1.43 p,m region are shown in Figure lb, and high-reso- z. lution spectraof the 2.2-2.5 pm region are shown in Fig- ure lc.

Modified Gaussianmodel and modeling approach The MGM of Sunshineet al. (1990) statesthat for a given position (pm) absorption with there is a distribu- oE tion in energy (x) with a standard deviation (o) and am- plitude (s). This is given by the equation E o | - E m(x): sexP[-(x p-t)2/2o2] CI where ru (x) is the modified Gaussianexpressed as a func- 3 E tion of energy.In reflectancespectra, as in transmission E spectra, absorption obeys the Beer-Lambert law. To es- o 2, tablish a linear system of additive, overlapping absorp- tions the reflectancedata are first converted to natural log reflectance,and the dependentvariable is energy (cm-'). However all data and results will be presentedas a func- ttbvelengthIn pn tion ofwavelength for consistencyand clarity. The effects Fig.2. RepresentativeMGM solutions applied to sample l l of multiple scattering,Fresnel reflectance, and low-energy for each ofthe spectral sampling resolutions. The solutions are wings of strong metal-O charge transfer absorptions in presented in natural log reflectance since the calculations are the ultraviolet are partially modeled by a straight line carried out in these units. In each plot the measuredand pre- continuum in energy.The model distributions are super- dicted spectraare shown as solid lines, and the residual spectrum line near the top of eachplot. imposed on this continuum. (data model) is shown as the solid The continuum is the dashedline. (a) A total of 18 model bands A nonlinear least-squaresalgorithm developedby Ka- are required to attain the MGM solution. The eight numbered per (1966) MGM to et al. is usedto determine solution bands are interpreted to model the well-resolvedelectronic tran- the spectra.This algorithm permits simultaneousanalysis sition and charge transfer absorptions. (b) The four labeled bands of the entire spectrum. Initial conditions for each band A, B, C, and D correspond the metal-OH stretching models of (position, width, strength)and the continuum are provid- the samedesignation presented by Burns and Strens(1966). An ed, and the fitting procedure incrementally adjusts the additional unlabeled band models absorption due to absorbed model parameters until possible improvement in fit is HrO. (c) The four model bands that are most strongly correlated negligible. The number of bands selectedfor initial pa- with mineral chemistry are labeled 1-4. rametersis determined from inspection of the refleclance spectra for resolved band minima and inflections. The 350 MUSTARD: ACTINOLITE ANALYSES FROM REFLECTANCE SPECTRA

TABLE1. Chemicalanalyses of actinolite

Sample 10 11 12 13 Oxidepercentages sio, 56.61 56.34 56.22 55.31 56.84 56.21 52.45 57.81 56.4s 55.43 58.15 54.86 Alro3 1.01 0.88 0.83 2.27 1.14 0.80 5.27 0.46 1.62 2.24 0.27 3.52 FerO. 1.95 1.70 2.62 0.41 0_43 0.60 3.36 0.27 0.38 0.62 o.23 0.58 FeO 3.72 3.98 3.49 4.67 2.47 5.70 7.45 2.65 5.55 5.39 2.41 4.13 Mgo 20.24 20.75 2080 20.80 2287 20.66 17.43 23.35 21.77 20.78 23.52 20.98 CaO 12.91 13.01 13.16 12.75 1205 12.61 11.79 13.63 12.21 1274 13.53 11 .83 MnO 0.37 0.28 0.31 0.29 0.11 0.11 0.53 0.29 0.34 0.34 0.31 0.16 Ct2o3 0.16 0.31 0.03 0.03 0.13 0,13 0.38 0.04 0.29 0.12 0.02 1.53 Na.O o.32 0.27 0.27 0.28 0.76 0.19 1.07 0.22 o.37 0.43 0.18 0.74 KrO 0.03 0.02 0.03 0.02 0.01 0.04 0.07 0.13 0.04 0.03 0.10 0.07 Total s7.32 97.54 97.76 96.83 96.81 97.05 99.80 98.85 98.94 98.12 98.72 98.40 Cationsper formulaunit Si 7.844 7.842 7.814 7.746 7.864 7.881 7.318 7.870 7.760 7.702 7.907 7.568 AI 0.166 0.144 0.136 0.375 0.186 0.132 0.867 0.074 0.262 0.367 0.043 0.572 FeP- 0.204 0.178 0.274 0.043 0.045 0.063 0.353 0.028 0.039 0.065 0.024 0.060 Fe2* 0.433 0.463 0.406 0.547 0.286 0.668 0.869 0.302 0.638 0.626 0.274 0.477 Mg 4.202 4.306 4.310 4.343 4.717 4.318 3.626 4.739 4.461 4.305 4.768 4.315 1.926 1.940 1.960 1.913 1.786 1.894 1.763 1.988 1.798 1.879 1.971 1.749 Mn 0.044 0.033 0.036 0.034 0.013 0.013 0.063 0.033 0.030 0.040 0.036 0.019 0.018 0.034 0.003 0.003 0.014 0.014 0.042 0.004 0.032 0.013 0.002 0.167 Na 0.086 0.073 0.073 0.076 0.204 0.052 0.289 0.058 0 099 0.116 0.047 0.198 K 0.005 0.004 0.005 0.004 0.002 0.007 0.012 0.023 0.007 0.005 0,017 0.012 Estimatedsite populations S(T) 7.88 7.84 7.81 7.75 7.86 7 88 7.32 7.87 7.76 7.70 7.91 7.57 A(T) o.12 0j4 0.14 0.25 0.14 0j2 0.68 0.07 0.24 0.30 0.04 0.43 Fe3*(T) 0.00 0.02 0.0s 0.00 0.00 0.00 0.00 0.03 0.00 0.00 0.02 0.00 A(M123) 0.05 0.00 0.00 0.12 0.0s 0.01 0.19 0.00 0.01 0.07 0.00 0.14 Fe3.(M123) 0.20 0.16 0.22 0.04 0.04 0.06 0.35 0.00 0.04 0.06 0.00 0.06 c(M123) o.02 0.03 0.00 0.00 0.01 0.01 0.04 0.00 0.03 0.01 0.00 0.17 Mg(M123) 4.20 4.31 4.31 4.34 4.72 4.32 3.63 4.75 4.46 4.30 4.77 4.31 Fe,-(M123) 0.43 0.46 o.41 0.50 0.18 0.60 0.79 0.25 0.46 0.56 o.23 0.32 Mn(M123) 0.04 0.03 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Fe*(M4) 0.00 0.00 0.00 0.05 0.11 0.07 0.08 0.05 0.18 0.07 0.04 0.12 Mn(M4) 0.00 0.00 0.00 0.00 0.00 0.00 0.06 0.03 0.03 0.04 0.04 0.02 Ca(M4) 1.93 1.94 1.96 1.91 1 79 1.89 1.76 1.92 1.79 1.89 1.92 1.75 Na(M4) 0.07 0.06 0.04 0.04 0.10 0.04 0.10 0.00 0.00 0.00 0.00 0.11 ca(A) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.07 0.01 0.01 0.05 0.00 Nofe.'Sampleorigins: 1,2, and 6: Brown TeachingCollection; 4 : Oaklawn,Rl; 5: Smithfield,Rl; 8: West Cummington,MA; 9: Warren County,NJ; 10: Cumberland,Rl; 11 : Chester,VT; 12: Lee, MA; 13: Lake Heneteh;17: OrangeCounty, CA; 18: Cassiar,8.C., Canada;19 : no. 14785 Berkeley,CA; 20 : Mueller 12ba, Quebec; 21 : USNM 44973, Cumberland,Rl; 9a, 99 : Porterville,CA. All chemicalanalyses conducted at Brown Universityexcept 19 (from Burns and Greaves, 1970), 20 (from Mueller, 1960), and 21 (from Mitchell et al., 1970). need for additional bands is indicated in the residual Low-resolution data. A total of l8 bands are required spectrum by a characteristic sinusoidal shape. The im- to attain a reasonablefit to all features (Fig. 2a). Seven plementationof the Kaper et al. (1966)algorithm allows are used for the OH bands, and three are used to fit the for selectivetoggling of band parametersto constrain so- edgeof the ultraviolet absorptionbetween 0.3 and 0.55 lutions (e.9., band width of OH overtone absorptions) pm. The remaining eight bands, labeled l-8 in Figure 2a, and assist in deriving solutions in complex systems of model the resolved chargetransfer and electronic transi- overlapping bands. tion absorptions. Ideally each band should be associated The MGM was applied to each of the spectra shown with a specific absorbing speciesin a specific site. How- in Figure l. Two criteria are used to determine when an ever, since the three octahedralsites Ml, M2, and M3 adequatesolution is achieved:(l) The total error ofthe are almost identical in size, we can anticipate a high de- fit is within a few tens of percent of the measurement gree of overlap in the Fe2*crystal field absorptions from error (0.250lo).(2) There are no systematic errors as a thesesites. Some of the model bands are almost certainly function of wavelength.Initially a complex spectrumwas combinations of electronic transitions from several sites. fitted iteratively, adding new bands until a residual error Nevertheless,they provide a consistentset of parameters (data model) satisfying criterion I was obtained. The for understandingthe relationship betweenchemistry and minimum number of bandsrequired to satisfythe second absorption in actinolite mineral spectra.Model parame- criterion has been used. The general shape and relative ters for the eight primary bands and the total error of the position of these bands are then used as initial starting fit are presentedin Table 2. parametersfor each of the remaining spectra.Each suite High-resolution OH overtones.The data in Figure lb ofspectra is treated separately,and representativemodel were fitted using band positions from Farmer (1974) and, solutions for sample I I are shown in Figure 2 for each of initially fixing band widths to lie between 6 and l0 cm-' the wavelength resolutions. (Burns and Strens.1966: Burns and Greaves.l97l). An MUSTARD: ACTINOLITE ANALYSES FROM REFLECTANCE SPECTRA 351 f aate 1-Continued

17 t8 19 9g Oxidepercentages 57.09 57.45 56.00 55.00 50.61 57.05 56.45 0.65 0.26 2.30 0.60 2.42 0.45 1.50 ()0, o.27 0.01 1.40 1.83 2.80 0.10 0.41 e o 5.80 4.96 4.22 19.60 19.90 5.46 5.01 -ct 2.61 22.00 20.65 21.76 20.00 11.00 8.26 o 12.24 13.22 11.10 10.00 10.82 1.58 11.90 o 0.33 0.29 0.11 0.29 2.69 0.22 0.29 -o 0.30 0.15 0.03 0.24 0.62 0.03 1.10 0.24 0.48 0.07 0.08 0.05 0.02 0.10 0.01 0.14 0.01 0.04 98.00 9815 96.34 98.s8 98.13 9758 97.92 Cationsper formulaunit 7.927 7.932 7.848 8.051 7.655 7.905 7.803 0.106 0.042 0.380 0.104 0.431 0.073 0.244 0.e0 u0 tto tto alo 0.028 0.001 0.148 0.202 0.319 0.010 0.043 Wavelengthin pm 0.673 0.573 0.495 2.399 2.517 0.633 0.579 of actin- 4_274 4.479 4.178 2.400 1.863 4.671 4.534 Fig. 3. Orientedsingle crystal transmission spectra 1.821 1.956 1.667 1.568 1.754 1.719 1.762 olite from Goldmanand Rossman (1977). The a spectrum(solid 0.039 0.034 0.013 0.036 0.345 0.026 0.034 line)was measured parallel to the a axis,the B spectrum(dotted 0.033 0.016 0.003 0.026 line) parallelto the b axis, and the 7 spectrum(dashed line) 0.167 0.008 0.299 0.068 0.141 0.019 0.021 resolveabsorp- 0.009 0.004 0.018 0.002 0.027 0.002 0.007 parallelto the c axis.Transmission spectra can Estimatedsite populations tionsthat aresuperimposed and overlapping in reflectancespec- 7.93 7.93 7.85 8.05 7.66 7.91 7.80 tra ofparticulatesurfaces. Note the two resolvedFe3*-Fe2* charge 0.07 0.04 0.15 0.00 0.34 0.07 0.20 transferabsorptions near 0.7 pm. 0.00 0.03 0.00 0.00 0.00 0.01 0.00 0.04 0.00 0.23 0.10 0.09 0.00 0.04 0.03 0.02 0.15 0.20 0.32 0.00 0.04 0.03 0.02 0.00 0.00 0.00 0.00 0.03 High-resolution combination overtones. The data in 4.27 4.48 4.18 2.40 1.86 4.67 4.53 Figure lc were fitted using a continuum and six bands 0.63 0.49 o.42 2.30 2.52 0.33 0.36 0.00 0.00 0 00 0.00 0.21 0.00 0.00 (Fig. 2c). The continuum is a straight, horizontal line to 0.04 0.04 0.06 0.10 0.00 0.30 0.22 provide a base for the bands, five bands are used to fit 0.04 0.03 0.01 0-04 0.13 0.03 0.03 well-resolvedvibrational bands,and one band is used 1.82 1.92 1.67 1.57 1.75 1 67 1.75 the 0.10 0.00 0.26 0.07 0.12 0.00 0.00 to approximate the contribution due to the electronic 0.00 0.03 0.00 0.00 0.00 0.05 0.01 transition band. The four bands that are most highly cor- related with composition are numbered. As with solu- tions to the overtone region of the stretching fundamen- tals, the model convergesrapidly and consistently to a solution. Model parameters for the four primary bands and the total error ofthe fit are presentedin Table 4. additional broad and shallow band was included to ac- Rnsur-rs cornmodate a diffuse absorption near 1.43 pm, probably due to adsorbedHrO (Burns and Greaves,l97l). The Low-resolution data continuum is a straight line segmenttangent to the spec- The position, strength, and width of the model bands tra on either side ofthese absorptions(Fig. 2b). Since the were compared with published polarized transmission positions and widths of the OH overtone absorptionsare spectraof actinolite (Burns, 1970; Goldman and Ross- expectedto be independent of chemistry in a binary sys- man. 1977'.Hawthorne, l98l). Polarized transmission tem (Burns and Strens,1966; Burns and Greaves,l97l; spectraoforiented samplescan resolve bands that over- Wilkens, 1970),the widths and positionsof bandsA, B, lap and are superimposedin reflectancespectra. Trans- C, and D were initially fixed and only the strengthswere mission spectraof actinolite, reproduced from Goldman allowed to vary. The continuum as well as the position, and Rossman(1977), are shown in Figure 3' Comparison strength,and width of the extra broad band were allowed of the model bands shown in Figure 2a with the trans- to vary freely. Following initial convergenceof the model, mission spectrashown in Figure 3 indicates a qualitative these constraints are relaxed to remove any remaining agreementin the number and position of absorptionsand error (Fig. 2b). Using the overtone region to model the bands. OH stretching absorption quantitatively allows the con- Bands I and 2 model the Fe2+-Fe3+charge transfer ab- tinuum and absorption due to adsorbedHrO to be mod- sorptions. Fe3*shows a preferencefor the M2 site, which eled with free parameters.This overcomes some of the shares an edge with all three other sites. However, the criticisms of Law (1976) regarding this method of anal- positions of the M2 and M4 sites are probably too far ysis for the fundamental region. Model parameters for apart, relative to the distance between the center of the the four primary bands and the total error of the fit are M2 site and the Ml and M3 sites,to be much of a factor. presentedin Table 3. It is unknown whether a given band (l or 2) is uniquely 352 MUSTARD: ACTINOLITE ANALYSES FROM REFLECTANCE SPECTRA

TABLE2. Model parameters for electronic absorptions

Sample Cen' wid* Strf Cen Str Cen Str 1 668.96 253.7 -0.474 742.25 129.8 -0.061 914.17 18ti.0 -0.135 1032.66 425.7 -0.592 2 656.97 248.1 -0.515 745.53 139.9 -0.112 908.31 185.3 -0.168 1032.66 425.7 -0.679 4 672.48 250.3 -0.391 73'1.27 111.0 -0.035 916.67 187.6 -0.083 1023.32 425.7 -0.558 5 651.20 237.8 -0.494 737.78 124.9 -0.112 894.33 195.4 -0.181 1031.24 430.2 -0.570 6 617.01 103.8 -0.029 686.61 157.9 -0.119 896.00 150.0 -0.075 992.92 378.0 -0.217 7 660.88 187.0 - 0.302 752.10 118.0 -0.082 904.82 228.0 -0.168 1055.43 449.7 -0.442 8 619.04 254.0 -0.808 739.02 150.8 -0.308 880.59 175.5 -0.306 1030.45 436.7 -0.744 9 656.20 204.0 -0.107 742.53 100.2 -0.031 904.85 197.9 -0.063 1029.95 408.9 -0.272 10 652.97 246.9 -0.531 746.25 1'13.2 -0.061 908.63 187-1 -0.158 997.19 403.9 -0.480 11 631.36 247.2 -0.573 739.90 143.7 -0.221 887.45 182.1 -0.235 1046.41 436.8 -0.623 12 591.40 225.0 -0.113 722.68 150.0 -0.076 907.82 175.0 -0.037 1009.84 393.9 -0.250 13 617.01 103.8 -0.1s0 683.41 127.2 -0.166 977.10 ',t46.4 -0.110 999.74 396.7 -0.353 17 658.34 217.9 -0.426 686.18 206.7 0.000 887.70 170.4 -0.112 1029.74 468.5 -0.583 1I 629.81 99.3 -0.116 715.68 110.3 -0.091 878.37 175.0 -0.108 1048.23 423.7 -0.348 19 644.23 198.8 -0.251 739.38 159.4 - 0.082 878.40 100.0 -0.030 977.49 415.8 -0.360 20 659.76 276.5 -1.432 770.62 142.9 -0.315 909.86 166.5 -0.581 1056.52 415.3 -1.312 21 656.79 300.1 -1.337 770.62 157.7 -0.257 909.86 165.4 -0.431 1056.52 454.2 - 1.065 9a 585.99 179.0 -0.001 702.74 160.7 -0.001 809.55 380.6 -0.001 873.66 80.7 -0.0s6 99 585.99 179.0 -0.120 702.74 160.7 -0.158 968.96 405.1 -0.336 1050.37 97.2 -0.055 'Center in nanometers. .. Width in nanometers. f Strength in log absorptions. associatedwith a particular site occupancy.The strength Bands 3 and 4 are interpreted here to model Fe2*elec- of charge transfer absorptions is thought to be propor- tronic transitionsin the Ml. M2. and M3 sites.Because tional to the product of the concentration of donor and the overall sizeand symmetry of thesethree sitesare very acceptorions (Smith and Strens,1976). The total areaof similar, the magnitudeof the d-orbital splittingsand hence bands I and 2 increaseswith the product of concentra- the energiesand probabilities of absorption will be more tions of Fe2* and Fe3* ions (Fig. a). Although there is a or less equivalent. Also, since the electronic transitions monotonic increase in log area of absorption and the in these sites are expectedto occur between the equiva- product ofconcentrations ofFe2" and Fe3*,it appearsin lent energy levels, the widths of the absorptions will be Figure 4 that there is a rapid increasein band area at low comparable (Burns, 1970; Marfunin, 1979), and it will values of the Fe2+-Fe3+concentration product, and the thereforebe difficult to resolveindividual absorptionswith rate ofincrease in band areawith increasingvalues ofthe these data. The strength ofband 5 is strongly correlated Fe2+-Fe3+concentration product is less. with the strength of band 8, with a correlation coemcient

Tlele 3. Model parameters for overtones of OH stretching absorptions

Sample Cen- wid* Strt 1" tet 1 1391.88 4.58 -0.4195 1397.62 5.09 -0.3212 1404.46 5.08 -0.0828 1412.49 5.09 -0.0212 0.0053 2 1392.14 4.55 -0.2861 1397.82 5.25 -0.2156 1404.35 s.08 - 0.0610 14',t1.755.09 - 0.0094 0.0060 4 1391.81 4.63 -0.5100 1397.60 4.70 -0.3713 1403.89 5.08 -0.1002 1409.80 5.09 -0.0229 0.0063 J 1392.14 4.55 -0.2861 1397.82 5.2s -0.2156 1404.35 5.08 - 0.0610 14',t1.755.09 -0.0094 0.0060 o 1391.46 4.85 -0.4479 1397.31 4.94 -0.2423 1404.33 5.08 -0.0410 1411.48 5.09 -0.0100 0.OO77 1396.12 4.50 -0.2988 1401.73 4.75 -0.2563 1408.25 5.08 -0.0710 1415.33 5.09 -0.0096 0.0080 I 1392.00 4.50 -0.1063 1397.91 5.49 -0.1084 1404.64 5.08 -0.0551 't411.44 5.09 -0.0279 0.0059 o 1392.14 4.62 -0.3344 1397.67 4.33 -0.1868 1403.29 5.08 -0.0261 1405.39 5.09 -0.0005 0.0037 10 1392.13 4.55 -0.2310 1397.79 5.25 -0.1646 1404.19 5.08 -0.0507 1410.52 5.09 -0.0105 0.0072 11 1396.13 4.55 -0.1810 1401.79 5.25 -0j447 1408.19 5.08 -O.O424 1414.52 5.09 -0.0085 0.0027 12 1392.15 4.77 -0.3133 1357.76 4.29 -0.1688 1403.54 5.08 -O.O222 1412.32 5.09 -0.0006 0.0023 13 1396.23 4.58 -0.3215 140't.73 5.45 -0.2099 1408.19 5.08 -0.0469 1414.26 5.09 -0.0107 0.0033 17 1392.03 4.55 -0.3048 1397.66 5.25 -0.2591 1404.49 5.08 -0.078/. 1411.63 5.09 -0.0165 0.0043 18 1391.88 4.60 -0.2407 1397.62 4.65 -0.2594 1404.24 5.08 -0.1008 1411.86 5.00 -0.0212 0.0040 19 1392.02 4.55 -0.1720 1397.69 5.25 -0.1 117 1404.35 5.08 -0.0216 1411.67 5.09 -0.0031 0.0042 20 1395.61 4.55 -0.0304 140t.80 5.25 -0.1531 1408.79 5.08 -0.1916 1416.88 5.09 -0.1056 0.0049 21 1391.68 4.55 -0.0156 1397.93 5.25 -0.0673 1404.84 5.08 -0.1020 1412.84 5.09 -0.0761 0.0049 9a 1392.27 5.28 -0.2489 1397.64 5.94 -0.1218 1405.24 5.08 -0.0166 1410.84 5.09 -0.01M 0.0034 9g 1392.59 5.01 -0.5895 1397.99 4.89 -0.3648 1403.M 4.85 -0.0845 1409.48 5.09 -0.0080 0.0055 'Center in nanometers. -- Width in nanometers. t Strength in log absorption. MUSTARD: ACTINOLITE ANALYSES FROM REFLECTANCE SPECTRA 353

TABLE2-Continued

Res Cen wid Str Gen wid Str Cen wid Str Cen wid Str oh rct 1 1040.85 97.O -0.133 1392.40 421.5 -0.093 2112.36 320.0 -0.035 2483.15 475.0 -0.314 0.0099 1042.62 90.6 -0.140 1392.40 421.5 -0.097 2090.00 320.0 -0.050 2486.23 475.0 -0324 0.0093 4 1041.28 90.6 -0.103 1399.26 421.5 -0.083 2046.28 320.0 -0-044 2484.77 490.4 -0.374 0.0092 1034.01 106.8 -0.192 1394.18 401.7 -0.082 2136.80 358.1 -0.064 2485,12 473.0 -0.324 0.0079 o 1026.88 138.2 -0.273 1292.76 676.9 -0.059 20s5.78 404.3 -0.140 2486.55 472.0 -0.475 0.0097 1037.97 108.2 -0.187 1511 .65 3677 -O.O44 2070.19 395.3 -0.051 2484.63 475.0 -0.324 0.0055 8 1030.48 82.7 -0.053 1389.12 491.5 0.204 2069.29 271.3 -0.023 2485.01 497.8 -0.225 0.0061 q 1042.62 90.0 -0.060 1313.62 671.7 -0.029 2071.87 343.9 -0.059 2485.77 400.0 -0.260 0.0071 10 1029.88 109.6 -0.199 1261.19521.0 -0.170 2172.91 416.3 - 0.078 2483.88 495.0 -0.384 0.0082 11 1033.86 97.1 -0.091 1429.02 417.8 -0.125 2056.51 368.9 -0.041 2487.91 485.0 -0.265 0.0077 12 1039.39 77.2 -0.049 1259.46 890.0 -0.074 2082.95 318.1 -0.076 2485.58 400.0 -0.260 0.0073 13 1031.62 115.4 -0.286 1230.45 601.1 -0.043 1889.1 0 460.0 -0.107 2467.15 700.3 -0.519 0.0060 17 1041.93 96.9 -0.098 1524.72 421.5 -0.060 2046.28 320.0 -0.044 2482.32 490.4 -0.374 0.0116 '1344.19 18 1041.08 150.0 -0.000 784.1 -0.102 2030.26 556.5 -0.181 2484.74 400.0 -0.356 0.0082 19 1036.42 89.3 -0.086 1269.51 612.3 -0.099 2118.05 408.9 -0.050 2486.99 400.0 -0.260 0.0067 20 1039.40 113.1 -0.238 1376.23 612.0 -0.445 2083.71 272.7 -0.039 2483.76 484.1 -0.437 0.0084 21 1039.40 124.5 -0.093 1375.55 702.7 -0.516 2013.98 278.4 -0.014 2483.76 484.1 -0.188 0.0080 9a 960.65 168.1 -0.618 996.68 586.6 -0.145 1923.81 389.9 -0.062 2435.00 655.0 -0.728 0.0080 9g 989.73 194.6 -0.578 1192.39 449.3 -0.092 1857.42 250.0 -0.020 2477.10 738.4 -0.690 0.0082

of0.94 (Fig. 5). The shape,position, correlated strengths, of Fe2t per formula unit (pfu), no individual band is a and relationship to the amount of Fe2+in the M4 site (see sensitive indicator ofthe concentration ofa specific ele- Table l) indicate that these two bands model the elec- ment in the actinolite structure. This is not surprising tronic absorptions associatedwith Fe2+in the M4 site. since site populations and the relative strengthofabsorp- This is the strongestassignment of model bands to spe- tion bands are expectedto be variable. From Beer's law, cific electronic processesthat can be made in this analy- absorption is an exponential function ofabsorption coef- sls. ficient. Therefore the log of absorption should be pro- Correlations betweenthe log areasof MGM bands (to- portional to the concentration ofthe absorbing speciesin tal probability of absorptions) and major element con- the site or sites responsiblefor the model band. It is ap- tents were computed. Although there are weak linear parent that the log area ofband 5 is proportional to the trends between some band parameters and the amount amount of Fe2+in the M4 site.If the log areaof bands3,

TABLE4. Model parameters for combination overtones of OH absorptions

Res Sample Cen. wid.. Strt Cen wid Str Cen wid Str Cen wid Str Y" ret 1 2291.10 37.70 -0.3193 2297.74 13.16 -0.1608 2317.34 23.25 -0.4866 2386.36 22.72 -0.3159 0.0052 2 2290.68 38.43 -0.3743 2298-3't 13.11 -0.1967 2317.70 23.50 -0.5735 2386.35 22.72 -0.3531 0.0040 4 2292.85 38.43 -0.5336 2296.29 13.11 -0.1066 2316.99 23.50 -0.6307 2386.03 22.72 -0.4031 0.0065 2294.22 38.43 -0.2156 2298.83 13.11 -0.0963 2318.96 23.50 -0.2816 2387.O1 22.72 -0.1864 0.0030 2286.36 36.08 -0.2071 2289.81 13.32 -0.1899 2313.28 24.54 -0.5733 2386.13 24.86 -0.2541 0.0084 2286.37 38.43 -0.0593 2294.46 13.11 -0.0505 2313.49 23.50 -0.1418 2386.36 21.83 -0.0624 0.0021 I 2288.86 38.43 -0.2838 2297.95 13.11 -0.1625 2316.96 23.50 -0.4487 2386.55 22.72 -0.2322 0.0068 q 2292.50 38.43 -0.2131 2298.70 13.11 -0j220 2318.47 23.50 -0.3323 2386.93 22.72 -0.2094 0.0024 10 2303.79 48.83 -0.1891 2297.33 8.34 -O 0287 2322.33 25.86 -0.0866 2388.42 22.72 -0.1098 0.oo24 11 2282.71 28.27 -0.1796 2298.38 15.89 -0.2514 2316.67 20.82 -0.3797 2384.73 22.73 -0.2414 0.0053 12 2296.s4 46.'t4 -0.1654 2297.63 11.29 -0.0590 2318.54 23.47 -0.1603 2386.77 22.72 -0.1237 0.0018 13 2293.74 39-97 -0.1698 2297.40 11.79 -O.O724 2318.78 26.83 -0.2288 2387.18 22.72 -0.1499 0.0019 17 2283.52 29.92 -0.1988 2298.27 15.19 -0.2439 2316.45 21.38 -0.4026 2384.70 21.84 -0.2404 0.0050 18 2288.80 38.43 -0.1225 2297.68 13.11 -0.0934 2316.61 23.50 -0.2234 2385.92 22.72 -0.1308 0.0018 19 2294.1s 48.39 -0.2120 2298.26 12.92 -0.1053 2318.68 24.12 -0.2623 2386.52 22.72 -0.1923 0.0024 20 2294.01 43.50 -0.1972 2298.41 13.11 -0.0966 2319.49 25.68 -0.2755 2387.36 22.72 -0.1933 0.0028 21 2294.21 48.39 -0.1038 2297.71 12.92 -0.0547 2317.46 24.12 -0.1408 2386.47 22.72 -0.0864 0.0025 9a 2315.24 54.99 -0.2205 2304.74 18.56 -0.0346 2332.16 28.67 -0.1097 2399.13 36.93 ^0.1423 0.0023 9g 2321.21 52.03 -0.2091 2304.24 17.51 -0.0288 2337.61 27.83 -0.0605 2403.36 37.10 -0.1306 0.0028 * Center in nanometers. .- Width in nanometers. t Strength in log absorption. 354 MUSTARD: ACTINOLITE ANALYSES FROM REFLECTANCE SPECTRA

120. 250. 6l *,* ! c o 90. 2o0. @ o IF ! ! c 60. c o o 150. ID (D *tt o * 50. o * o ** o 100. L o rF* o L *j* o.o o.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 50. IF Fe2**FeS* Fig.4. The areaofmodel bandsI and 2 plottedagainst the o. productof Fe'?*and Fe3*concentrations. Note the distinct in- o. 20. 40. 60. 80. 100. creasein strengthof thesecombined bands with increasingval- uesof the productof Fe'z*and Fe3*concentrations. Areo of Bond 5 Fig. 5. The areaofmodel band8 plottedagainst the areaof 4, and 6 is proportional to the amount of Fe2t in the Ml, modelband 5. Thesebands are interpreted to modelFe2* elec- M2, and M3 sites (or some combination of sites) then a tronictransitions in theM4 site(Goldman and Rossman, 1977), linear equation relating band areas to sample chemistry and the stronglypositive correlation is consistentwith this hy- can be established: pothesis. C.AB + C*4oo* Cy4o, t C+4* + C : Fe'?*Pfu where C,, Cr, Cr, and Co are proportionality coefficients volving complex overlapping absorption bands in reflec- for the log areas(,40) of bands3,4,5, and 6. The constant tance spectra.Ultimately it may be possible to associate C, accountsfor any systematicerrors in the MGM solu- particular bands with site occupancies.The high corre- tions. Empirically derived values for these proportional- lation between predicted and actual Mg# and Fez* pfu ity coefficientsare C, : 3.19 x 10-3,C2: 1.45 x l0 3, shows that the MGM can be used as a high-quality tool C. : 3.10 x l0-3,Co: 7.20 x l0-3,and C, : -4.69 x for remote compositional analysis and can provide non- l0-'z with a root mean squareerror of 0.11 ions. Actual destructive estimates of mineral composition in labora- and predicted Fe2* pfu using this relationship are pre- tory applications. sented in Table 5 and illustrated in Figure 6a. Similar overtones equation relating the Mg/Fe ratio to band areascan also OH be established.Empirically derived proportionality coef- Burns and Strens (1966) established the geochemical ficients for the Mg# lX-"/(X-" * X.")l are C, : 2.9 x and crystallographic origin of four OH stretching fun- l0 5,C2:4.72 x 10o, C3:3.87 x l0-0,C+: 1.65x damentals in Fe-Mg ortho- and clinoamphiboles. The l0-3, and Cr: 1.007 with a root mean squareerror of proportion of Fe2* and Mg in the Ml and M3 sites de- 0.024, and the resultsare presentedin Table 5 and Figure termines the band positions of the fundamental stretch- 6b. ing bands. Using transmission spectra,Burns and Strens The systematic nature of the MGM solutions and the ( I 966) also establisheda relationship betweenthe relative relationship of bands to known absorptions indicate the strengthsofthe bands and proportional concentration of MGM shows significant promise as a method for decon- Fe2*and Mg in the Ml and M3 sites.These relationships

TABLE5. Actual and calculated p"z* pfu and Mg numbers

sample 1 2 4 5 6 7 I I 10 11 12 13 17 18 19 20 21 9a 99 FeE*pfu trom electronicabsorptions Act 0.43 0.46 0.40 0.54 0.28 0.66 0.86 o.3o 0.63 0.62 0.27 0.47 0.67 0.54 0.49 2.39 2.51 0.63 0.57 Calc 0.54 0.61 0.47 0.54 0.34 o.4o 1.02 0.21 0.78 0.68 0.34 0.36 0.45 0.51 0.45 2.35 2.45 0.61 0.62 Correlationcoefficient : 0.9825 Mg number from electronic absorPtions Act 0.86 0.87 0.86 0.88 0.93 0.85 0.74 0.93 0.86 0.86 0.94 0.88 0.85 0.88 0.86 0.47 0.39 0.87 0.87 Calc 0.86 0.84 0.87 0.87 0.93 0.90 0.75 0.94 0.81 0.83 0.91 0.91 0.87 0.87 0.88 0.45 0.42 0.88 0.87 Correlationcoefficient : 0.9854 Mg number trom OH overtone absorptions Act 0.86 0.87 0.86 0.88 0.93 0.85 0]4 0.93 0.86 0.86 0.94 0.88 0.85 0.88 0.86 0.47 0.39 0.87 0.87 Calc 0.78 0.78 0.78 0.78 0.84 0.77 0.66 0.85 0.78 0.77 0.85 0.80 0.76 0.71 0.82 0.40 0.36 0.84 0.82 Correlationcoefiicient : 0.9808 MUSTARD: ACTINOLITE ANALYSES FROM REFLECTANCE SPECTRA 355

I Fe,*(Ml,M3): lB' + 2C' + 3D, ) Mg,*(Ml,M3):3A' + 28' + lC, 2.5 wherel', B', C', andD' are the relativestrengths of each I, a) band, normalizingthe sum of the strengthsto 1.0.It fol- +.r 2.O lows that an estimate of the Mg# o can be obtained by = o Mg#: (3A, + 28' + C')/3.0. o 1.5 o For this relationship to be an accurate representationof the true Mg#, ion distribution must be random and con- + N 1.O tributions to the intensity q) of the fundamental absorptions L must be primarily from Fe2*and Mg (Strens, 1974 Law, 1976).These principles will be applied to the data pre- o.5 sented in Figure lb using the MGM to determine the * strengths of the four bands. The analysis of Burns and a Strens(1966) and most subsequentapplications of the o.0 relationship have used transmission data obtained in the 0.0 0.5 1.O 1.5 2.O 2.5 wavelength region of the fundamental stretching absorp- tion (2.7-2.8 prm).Presented here is one of the few ap- Fez+p.f.u. plications of this technique to high-resolution reflectance spectrameasured of the overtone absorptionsnear 1.4 o pm. g .9 *tt The Mg#'s calculatedusing the strengthsof absorptions o- o.9 L A, B, and C determined with the MGM model are pre- gto sented in Table 5 and Figure 7 along with the Mg# de- o o.8 termined from chemical analyses.These calculated Mg#'s have a correlation coefficient of 0.971 with the actual .9 c o.7 Mg#. The samplesthat plot away from the highly corre- o lated grouping are readily explained from site population L o arguments.Samples 9a and 99 have higher Mg#'s because o o.6 they have a large proportion of available Fe2*in the M4 tr site and thereforeless in the Ml and M3 sites.Sample E o.5 18 has o a lower than expected Mg# becausethere is no L rF rF Fe2"in the M4 site and therefore more Fe2*available for o.4 the Ml and M3 sites.These samples :h violate the assump- or tion that the ions of Fe2* and Mg are randomly distrib- b o.3 uted in the M sites. o.3 0.4 0.5 0.6 0.7 0.E o.9 The calculated Mg#'s underestimate the Mg#'s deter- mined analytically.Wilkens (1970), Strens(1974), and Mgf from Chemistry Clark et al. (1990) all observeda systematicoveresti- mation of the amount of Fe2+in the Ml and M3 sitesin Fig. 6. Estimates of Fe content and MglFe ratios in the ac- similar analyses.The simplest explanation is that in cal- tinolite samplesfrom the areaof absorption. (a) Amount of Fer* pfu rgainst cic amphiboles Fe2*is much more abundant in the Ml determined analytically and plotted the amount of Fe'z*(calculated) predicted from a linear and M3 sitesbecause Ca fills the M4 site and Fe2+avoids combination of the ar- eas of the model bands 3, 4, 5, and 6. Me# determined an- the M2 site. However the amount of Fe2* predicted in O) alytically and plotted against the Mg# (calculated) predicted from the Ml and M3 sites exceedsthe total amount of Fe2*in a linear combination of the areas of the model bands 3, 4, 5, somesamples. Clark et al. (1990)postulate that the effects and 6. The values used to create these plots are given in Table of multiple scatteringincrease the apparentdepths of weak 5. The solid line in each plot indicates a l:l correlation. bands relative to strong bands, thereby skewing the cal- culations toward lower Mg# estimates. This hypothesis predicts that estimatesof Mg#'s for sampleswith high Fe sentially reduces the apparent strength of the Mg-OH rel- should be overestimated.This is not the case,as samples ative to the Fe-OH absorptions. A similar effect can be 20 and 2l follow the same trend as the low-Fe samples. seen in the strengths of the combination overtone bands It is observed that samples with higher Fe also have in the wavelength region of 2.2-2.4 pm, where samples steeper spectral slopes toward longer wavelengths near with the strong 2.4-1rm electronic transition bands (sam- 7.4 p,m(Fig. la, Table l), causedby the long wavelength ples 9a, 99, 13) have the weak combination overtone bands wings of Fe2* electronic transition absorptions. This es- relative to samples with weak 2.4-p.m electronic absorp- 356 MUSTARD: ACTINOLITE ANALYSES FROM REFLECTANCE SPECTRA

l.OOO l* o.9 * ** o.E2s e o.E IF o + o (' 0.650 CL rf a o.7 rF rF E O..+75 e o.6

:h 0.500 L- o o.5 2342- 23EE. 2394. 2400.

Center of Bond 4 o.4 * Fig. 8. The centerof band4 plottedagainst the Mg# deter- minedanalytically. The positionof this bandis a sensitivein- o.5 r- dicatorof FelMgratios for tremolite-actinolitesolid solution. 0.3 o.4 0.5 0.6 0.7 o.E o.9 1.0

Mgf from Chemistry there is a high degree of overlap between these bands, there is a greater uncertainty in the band position deter- Fig. 7. Mg# determinedanalytically and plottedagainst the mined by the model. Band 4, however, is not affectedby predicted ofBurns and Strens(1966) Mg# usingthe techniques the complications of overlapping bands, and the position on the first overtoneof the OH stretchingfundamental. The of this band models a very sensitive indicator of the Fe/ valuesused to createthis plot aregiven in Table5. Mg ratios in these samples. The position of band 4 shifts approximately 40 cm ' tions(samples9,12, l8). Eventhough the Mg bandsare from low Fe (sample 12) to high Fe (sample 20). Bata- enhancedby multiple scattering,as the amount of Fe in- banov et al. (1974) document a shift of approximately creasesthe increasein slopedecreases the relative strength l0-15 cm-' acrossa comparablecompositional range in of these bands. Therefore even the predicted values for the position of fundamental bending mode minima. The high-Fe samplesare too low. remaining 25-30 cm-' is contributed by the differencein wavelength between the dominant stretching mode ab- Combination oYertones sorption in low-Fe samples(A) and high-Fe samples(C). The associationbetween the OH combination overtone A continuous rather than discrete shift in band position bandspositioned between 2.2 and 2.5 pm and composi- is observed becausecontributions from individual tion is less well understood than the stretching funda- stretching modes are not resolved with the sampling res- mentals and overtones. These bands are thought to be olution used to acquire these data. combination overtonesinvolving the metal-OH- bending The width of band 4 increasesfrom approximately 80 'in modes centered near 650 cm-' and the OH- stretching cm 'in sample12 to 130cm sample2l for a total '. modescentered near 3750 cm-'(Hunt, 1977).From Fig- increaseof about 50 cm Analyses of fundamental vi- ure lc, three well-resolved band minima and a shoulder brational absorptions (Burns and Greaves, l97l Bara- near 2.26 pm, indicating the presenceof a fourth band, banov et al. 1974)and of the 1.4-trmovertone bands in are observed in all spectra. Minor bands of variable in- this study indicate no systematicchanges in band widths tensityand importanceoccur tear 2.25 p,m,2.35pm, and with changingcompositions. However, the differencebe- at wavelengths longer than 2.4 pm. Variations in band tween the wavelength positions of the wings of the com- strength are due primarily to the relatively intensity of bined absorptionsin the 1.4-pm region for samples12 the 2.4-pm electronictransition band (e.g.,samples 9a and 2l is also approximately50 cm-'. Thereforethe in- and 99 have the strongest 2.4-pm electronic absorption creasein width of the combination overtonesis simply a bands and the weakestcombination overtone bands).The consequenceofthe increasein the relative strengthofthe vibrational bands become broader and the band minima FeFeMg and FeFeFe stretching fundamentals and of the move to longer wavelengthswith increasingFe. fact that individual overtones of the stretching funda- Correlations of the model parameters with composi- mentals are not resolved with 2-nm spectral resolution tion were computed, and it was found that the positions used to acquire these data. of bands 2,3, and 4 were most stronglycorrelated with Therefore, the majority of the systematic changesin the FelMg ratios and the total amount of Fe2*.Band 4 is absorption width and band positions are contributed by the most highly correlated with the Fe/Mg ratios, and a the well-understood changes in number and relative plot of the position ofband 4 againstthe Mg# determined strength of fundamental bending mode vibrations. Two from chemical analysisis presentedin Figure 8. The other simple predictions can be made based on this result: the bands may be as highly correlatedwith the Mg#, but since width of the combination overtone absorptions will nar- MUSTARD: ACTINOLITE ANALYSES FROM REFLECTANCE SPECTRA 357 row and band positions will continue to shift to longer for absorptionsdue to adsorbedHrO. Although the actual wavelengthsas the Mg#'s of samplesprogress Io zero. Mg# is systematically greater than the calculated Mg#, this approach is nondestructive, requires little sample Discussionand conclusions preparation, and can be corrected simply for the system- The reflectance spectra of the minerals studied here atic difference between the actual and calculated Mg#'s. reflect the flexibility of the crystal structure. It must be noted, however, that this method has only This structure can accommodate a wide range of com- been tested on simple chemical systems.The presenceof positions in many different ordering and site-population appreciableamounts of Al3* and Fe3*in the Ml and M3 configurations, even in minerals of the relatively simple sites, or Na and K in the A sites,results in an increasein tremolite-actinolite-ferroactinolite solid solution series the number or position of the stretching fundamentals examined in this analysis.Nevertheless the results of the (Burns and Greaves, 1971). These absorptionsoverlap MGM model applied to reflectancespectra of thesemrn- significantly with the (Mg,Fe)-OH- absorptions. Howev- erals indicate that many of the complexities observedin er, the stretching fundamentals exhibit very low vari- thesedata can be examined through quantitative analysis ability in model band positions and widths. Through the of reflectancespectra. The number and position of the use of strict mathematical constraints on allowable band bands required to model features thought to be due to widths and positions, the difficulties of overlapping and electronictransitions and chargetransfers correspond well superimposedabsorptions in complex systemscould be with previous work on oriented crystal transmission addressed. spectra of similar minerals. For the analysesof the OH Results from the application of the MGM to the com- overtone absorption in reflectancespectra it was found bination overtone bands indicate that the positions of that the MGM model provided a constrained and con- these bands are sensitive indicators of the FelMg ratios sistent tool to quantify the systematicvariations in these of the minerals. It was found that the positions of the absorptions with chemistry. model bands move to longer wavelengthsand the widths Analysis of the areas of individual model electronic of the bands increasewith increasing Fe2+content. The absorption bands with composition indicates that no one position of the band centered near 2.4 rrm is the most band is a sensitive measure of the bulk composition of highly correlated with the Fe/Mg ratios of the samples, thesesamples. Because absorptions in the wavelengthre- partly becausethis band is isolated and model solutions gion examined are primarily due to Fe3*and Fe2*,most are better constrained. Both the broadening of the ab- of the individual bands exhibit weak linear relationships sorptions with increasing Fe and the shift in wavelength between area and the amount of Fe2*,whereas the total position are a function ofthe increasedcontributions of area ofall bands thought to be associatedwith electronic the C and D stretching fundamentalsto the combination transitions show a relatively high linear correlation with overtones. The stretching fundamentals are too closely the total amount of Fe2*in these samples.Because these spacedto be resolved in the combination overtones,but model bands are expectedto have different proportion- the increasedimportance of the Fe-OH bands is still ob- ality constants to composition, variability in site occu- served. pancy is anticipated to causescatter in the simple rela- tionships betweenband area and composition. Therefore AcrNowlnncMENTS a simple linear relationship was establishedto relate band The author is indebted to J. Sunshinefor permissionto usethe modified area of bands 3, 4,5, and 6 to the amount of Fe2*pfu Gaussianmodel and for many thoughtful discussionson the application and the Mg# using ditrerent proportionality constantsfor of the model and interpretation of results. I wish to acknowledgethe each band. This relationship provides a reasonably ac- contributions of S. Pratt for the acquisition of the reflectance spectra, J. curate estimate of the Fe content of the samples,especial- Devine for microprobe analysison the Keck microprobe facility at Brown University, R.G. Bums for lending several actinolite samples, and R. ly for applications to remote observations.It is likely that Gwinn for the FeO wet chemical measurements.I also wish to thank this relationship could be strengthened with increased R.G. Burns. C.M. Pieters. J.W. Head. P.C. Hess. and E.M. Parmentier knowledgeofactual site occupancyor refined calculations for their input on this manuscript. This researchwas supportedby NASA to take variablesite occupancyinlo account. gant NAGW-I I 18. RELAB is supponed as a NASA facility under grant number NAGW-748. The application of the MGM to the OH overtone and combination overtone bands provides a useful tool to RnrrnrNcns crrED quantify the systematic variations in band strength and position associatedwith chemical change. The method Adams, J.B. (1974) Visible and near-infrared diffuse reflectance:Spectra developed by Burns and Strens (1966) was used to cal- ofpyroxenes as applied to remote sensingofsolid objects in the solar 7 4829-4836. proportion system Journal of GeophysicalResearch, 9, culate the of Mg and Fe2*in the Ml and M3 Allen, G.C., and Hush N.S. (1967) Intervalence-transferabsorption. Part sitesand also the Mg#. This application is one of the few l. Qualitative evidencefor intervalence-transferabsorption in inorgan- to use reflectancespectra ofthe first overtone ofthe OH ic systemsin solution and in the solid state.In F.A. Cotton, Ed., Pro- stretching fundamental to characterizethe relative grams in Inorganic Chemistry, vol. 8, p. 357-389. Wiley, New York. (1969) strengths of these bands. It was found Bancroft, G.M., and Burns, R.G. Mdssbauerand absorption spec- that the MGM tral study of alkali amphiboles. Mineralogical Society of America Spe- provided a self-consistentestimate of the Mg# when an cial Paper,2,137-148. additional band was included in the analvsis to account Barabanov,A.V.,Znrina, M.L., and Sobolev,V.K. (1974)Infrared spectra 358 MUSTARD: ACTINOLITE ANALYSES FROM REFLECTANCE SPECTRA

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